Question

If the radius of a sphere is mentioned as $7\, m$ with an error of $0.02\, m$ then the approximate error in calculating its volume is

• A. $1.83 \pi m ^{3}$
• B. $2.25 \pi m^{3}$
• C. $4.39 \pi m ^{3}$
• D. $3.92 \pi m ^{3}$

Answer 1

Answer: (D)

Radius $(r)=7 m$
Error in radius $(d r)=0.02 m$
Volume of sphere $(v)=\frac{4}{3} \pi r^{3}$
differentiate w.r. to ' $r$ ' on both sides,
$\frac{d v}{d r}=\frac{4 \pi}{3}\left(3 r^{2}\right)$
$d v=4 \pi\left(r^{2}\right) \cdot d r=4 \pi(49) \cdot(0.02)$
$d v=3.92 \pi m^{3}$